The grades on a math midterm at Santa Rita are normally distributed with $\mu = 68$ and $\sigma = 5.5$. Kevin earned a $71$ on the exam. Find the z-score for Kevin's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Kevin's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{71 - {68}}{{5.5}}} $ ${ z \approx 0.55}$ The z-score is $0.55$. In other words, Kevin's score was $0.55$ standard deviations above the mean.